I don't think there is a 581 in the Pantone+ InDesign swatch book. It's an undocumented feature that Pantone built in. It wasn't a new color, so why not use the Pantone Solid Coated that shipped with InDesign?

I'm finding that the old PMS colors don't quite match up with the new PANTONE + versions of the same color (450 and 139 are good examples) and I'm creating a color standard that will be used by a company for years to come. I'm not sure just what the status is of Pantone + out in the field (is everyone switching to it? Will old PMS be obsolete?) so that's why I needed to create a swatch of 581 using the new Pantone + library.

If you’re using spot colours, then minor differences shouldn’t matter, since the colour definition in InDesign means nothing. If you’re printing using process colours then you shouldn’t be speccing spot inks. If the colours might be printed as either, depending on the job, then define them twice, once as a spot and once as a process and make sure the users understand which colours to use for a given output scenario. For that, pick the spot based on the most recent Pantone swatch books and pick a process colour to closely match the spot colour using any process colour guide, Pantone’s or anyone else’s. I would not use the Bridge, which I think is a waste of money. The benefit of using Pantone’s process guides is they are on the same stock and use the same coating as the spot colour guides.

But my CMYK values from PhotoShop CC 20014 are different than InDesign's......

Photoshop has always defined Pantone spot colors as Lab, so if you get CMYK values they are a color managed conversion from Lab to CMYK— the values vary depending on the destination CMYK profile.

Starting with CS6 InDesign and Illlustrator also use Lab definitions for the Pantone + Solid libraries, which are spot colors. The Pantone Color Bridge libraries use CMYK definitions and are process colors.